I. Field
The present disclosure relates generally to electronics, and more specifically to techniques for tuning resistors and capacitors.
II. Background
Resistors (R) and capacitors (C) are circuit components that are widely used in various types of circuits. For example, resistors and capacitors are commonly used in active RC filters, amplifiers, mixers, and so on. Resistors and capacitors are also fabricated on various integrated circuits (ICs) such as analog ICs and radio frequency ICs (RFICs).
Resistors and capacitors in a given circuit typically have specific values that are selected based on the requirements of the circuit. For example, in an active RC filter, the 3 dB bandwidth of the filter is determined by an RC product. Hence, the nominal values of resistors and capacitors in the filter are selected to achieve the RC product. However, the actual value of an on-chip resistor may vary by as much as 25% from the nominal R value, and the actual value of an on-chip capacitor may vary by as much as 15% from the nominal C value. The variations in resistance and capacitance are due to IC process manufacturing tolerance.
Large variations in resistance and capacitance may result in large variations in circuit characteristics and performance. As an example, the bandwidth of an active RC filter may vary by as much as −30% to +57% from the nominal bandwidth due to ±25% variation in resistance and ±15% variation in capacitance. This large variation in bandwidth is not tolerable for most applications, especially for higher order filters designed to meet stringent requirements.
Conventionally, large variations in resistance and capacitance are accounted for by adjusting only the capacitor. In one common tuning method, an RC time constant is formed by the product of an on-chip resistor and an on-chip adjustable capacitor. The RC time constant is tuned by varying the adjustable capacitor to achieve the desired RC time constant, which may be ascertained based on an accurate clock. For this tuning method, the adjustable capacitor compensates for the entire variation in resistance and capacitance, i.e., the entire spread in the RC product. To account for the worst case in which the resistor varies by −25% and the capacitor varies by −15%, the adjustable capacitor should be approximately 60% bigger than the size required if the resistor and capacitor had been constant over IC process.
Capacitors are very inefficient when fabricated in a standard silicon process since their density or capacitance per micron square is very low. Furthermore, most of the area of a circuit such as an active RC filter may be taken up by capacitors. Hence, tuning the active RC filter by adjusting only the capacitor may result in the filter area increasing by a large amount, e.g., about 60% for the example given above.
There is therefore a need in the art for techniques to account for large variations in resistance and capacitance in a more efficient manner.